$\dfrac{ -6s + 8t }{ -4 } = \dfrac{ -4s + 5u }{ 8 }$ Solve for $s$.
Multiply both sides by the left denominator. $\dfrac{ -6s + 8t }{ -{4} } = \dfrac{ -4s + 5u }{ 8 }$ $-{4} \cdot \dfrac{ -6s + 8t }{ -{4} } = -{4} \cdot \dfrac{ -4s + 5u }{ 8 }$ $-6s + 8t = -{4} \cdot \dfrac { -4s + 5u }{ 8 }$ Multiply both sides by the right denominator. $-6s + 8t = -4 \cdot \dfrac{ -4s + 5u }{ {8} }$ ${8} \cdot \left( -6s + 8t \right) = {8} \cdot -4 \cdot \dfrac{ -4s + 5u }{ {8} }$ ${8} \cdot \left( -6s + 8t \right) = -4 \cdot \left( -4s + 5u \right)$ Distribute both sides ${8} \cdot \left( -6s + 8t \right) = -{4} \cdot \left( -4s + 5u \right)$ $-{48}s + {64}t = {16}s - {20}u$ Combine $s$ terms on the left. $-{48s} + 64t = {16s} - 20u$ $-{64s} + 64t = -20u$ Move the $t$ term to the right. $-64s + {64t} = -20u$ $-64s = -20u - {64t}$ Isolate $s$ by dividing both sides by its coefficient. $-{64}s = -20u - 64t$ $s = \dfrac{ -20u - 64t }{ -{64} }$ All of these terms are divisible by $4$ Divide by the common factor and swap signs so the denominator isn't negative. $s = \dfrac{ {5}u + {16}t }{ {16} }$